The GAS tour has 2 days in the Berner Oberland. One day has some group activity but you can easily skip it and do more strenuous hikes in the area. Some people hiked on the free afternoon in Baden-Baden as well as the free afternoon in Hallstatt. I skipped going in to Neuschwanstein Castle (had been there before) and walked partway around the lake but it was not strenuous. On that day your choices are limited as you are seeing this area while you are in transit from the Lauterbrunnen Valley in Switzerland to Munich so the stop is just for a couple of hours. Some on my trip walked near Salzburg Castle which looked wooded but I did not go up there so can’t give you firsthand info.
The 21 BOE is a fabulous tour - really, my favorite out of the 10 I’ve done, but has quite a few cities. As a group we did around 10-12 miles on the full days in Amsterdam and Rome so you get plenty of walking in. Rome has tons of steps too, lol. There was a full day in Berner Oberland that is free. My guide had optional activities if people wanted to join him which included going to the top of the Schilthorn, then in the afternoon hiking from Mannlichen to Kleine Scheidegg (easy hike but just jaw-droppingly beautiful). Other guides might do things differently but hiking is doable on that day. This tour also stops at Neuschwanstein so some hiking could be squeezed in on that day. It’s NOT a transit day on this tour so you could hike out of Reutte if you wanted to skip the group activity. There are 2 nights/1 full day in Cinque Terre where some in my group hiked. Can’t think of any other opportunities for hikes on this tour.
Best of England had a couple opportunities. There is a free afternoon in Bath that you could use to hike a scenic vista hike (blanking on the real name right now) or take a long walk along the Kennet and Avon canal. There was a walk with the guide in the Cotswolds and then a free day in the Lake District where you could hike out of Keswick. I walked up to Castlerigg stone circle on my own altho most of it was along populated roads.
I’ve not done the Best of Italy.
In general I’d agree that the RS tours aren’t particularly hiking focused. While you could skip activities to hike in some instances, you might miss some neat sights.
To me I’d say the GAS tour offered the most opportunity for working hiking in.
I’ve also done hiking programs with Road Scholar. I did one in England although they appear to have changed the focus a bit. When I went it was focused on Iron Age hill forts. I thought this would be fascinating but in the end...you’ve seen one Iron Age hill fort, you’ve seen them all!